What is the next term in series 4, 6, 10, 14, 22, 26, 34, 38, 46, ___ ?

Concept: A number series can hide a simpler underlying sequence (such as primes, squares, or another familiar sequence) inside a scaled version of it. To decode it, apply the inverse of the scaling to every term, identify the simpler pattern, extend that pattern by one more step, and then re-apply the original scaling to obtain the next term.

1. Divide every given term by 2: 4/2 = 2, 6/2 = 3, 10/2 = 5, 14/2 = 7, 22/2 = 11, 26/2 = 13, 34/2 = 17, 38/2 = 19, 46/2 = 23.

2. The resulting sequence 2, 3, 5, 7, 11, 13, 17, 19, 23 is exactly the sequence of consecutive prime numbers.

3. The next prime number after 23 is 29 (24, 25, 26, 27, and 28 are all composite, so none of them break the run).

4. Reverse the halving used in step 1: multiply 29 by 2, which gives 58 as the next term of the original series.

Cross-check: Every consecutive pair among 2, 3, 5, 7, 11, 13, 17, 19, 23 skips no smaller prime (for example, between 19 and 23 the numbers 20, 21, and 22 are all composite), confirming the sequence is an unbroken run of consecutive primes. So the required next term must be twice the very next prime after 23, which is 58.